Add $ \dfrac{71}{30} $ and $ 2 $ to get $ \dfrac{ \color{purple}{ 131 } }{ 30 }$.

Step 1: Write $ 2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add fractions they must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{30}$.

$$ \begin{aligned} \frac{71}{30} +2 & \xlongequal{\text{Step 1}} \frac{71}{30} + \frac{2}{\color{red}{1}} = \frac{ 71 }{ 30 } + \frac{ 2 \cdot \color{blue}{ 30 }}{ 1 \cdot \color{blue}{ 30 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 71 } }{ 30 } + \frac{ \color{purple}{ 60 } }{ 30 }=\frac{ \color{purple}{ 131 } }{ 30 } \end{aligned} $$